SOLUTION: If a 17-ft. ladder is leaning against a building. The base of the ladder is 7 feet from the base of the building. How high up the side of the building is the top of the ladder?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: If a 17-ft. ladder is leaning against a building. The base of the ladder is 7 feet from the base of the building. How high up the side of the building is the top of the ladder?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 9616: If a 17-ft. ladder is leaning against a building. The base of the ladder is 7 feet from the base of the building. How high up the side of the building is the top of the ladder?
Answer by DWL(56) About Me  (Show Source):
You can put this solution on YOUR website!
This is a right triangle problem so we can use the Pythagorean Theorem that says: A%5E2%2BB%5E2=C%5E2
We know the ladder is 17 Ft. Tall and leaning against the wall and the bottom of the ladder is 7 Ft out from the wall.
So we will make the height of the wall where the top of the ladder is = A
The distance (7 Ft.) from the wall out to the bottom of the ladder = B
and the length of the ladder (17 Ft.) = C
So A & B are legs on the right Triangle and C is the hypotenuse of the Triangle.
Now we can solve the problem.
We now put the numbers in for the variables we know and the equation looks like this: A%5E2%2B7%5E2=17%5E2
Now we solve the equation, lets isolate A^2 by subtracting 7^2 from both sides:
A%5E2%2B7%5E2-7%5E2=17%5E2-7%5E2 so this becomes A%5E2=17%5E2-7%5E2
Now lets sqaure our numbers so: A%5E2=289-49 or A%5E2=240
Now lets lets get rid of the square on the A by taking the square root of both sides so: sqrt%28A%5E2%29=sqrt%28240%29 = A=15.49
Now we know the ladder is 15.49 Ft. up the side of the building.
Lets check it with our formula A%5E2%2BB%5E2=C%5E2
15.49%5E2%2B7%5E2=17%5E2 = 239.94%2B49=289 = 288.94=289 We will round up to 289. Close enough for goverment work.